# Peek's law

In physics, Peek's law defines the electric potential gap necessary for triggering a corona discharge between two wires:

${\displaystyle e_{v}=m_{v}g_{v}r\ln \left({S \over r}\right)}$

ev is the "visual critical corona voltage" or "corona inception voltage" (CIV), the voltage required to initiate a visible corona discharge between the wires.

mv is an irregularity factor to account for the condition of the wires. For smooth, polished wires, mv = 1. For roughened, dirty or weathered wires, 0.98 to 0.93, and for cables, 0.87 to 0.83, namely the surface irregularities result in diminishing the corona threshold voltage.

r is the radius of the wires in cm.

S is the distance between the center of the wires.

gv is the "visual critical" electric field, and is given by:

${\displaystyle g_{v}=g_{0}\delta \left(1+{c \over {\sqrt {\delta r}}}\right)}$

δ is the air density factor with respect to SATP (25°C and 76 cmHg):

${\displaystyle \delta ={\rho \over \rho _{SATP}}}$

g0 is the "disruptive electric field."

c is an empirical dimensional constant.

The values for the last two parameters are usually considered to be about 30-32 kV/cm (in air [1]) and 0.301 cm½ respectively. This latter law can be considered to hold also in different setups, where the corresponding voltage is different due to geometric reasons.

Note: The formula has an unintuitive implication that "if the distance between the wires is half the diameter (the radius) then the voltage needed for discharge is zero. Ln (1) = 0." I conclude that the distance is measured from the center of the wires. Not obvious in the definition of "S". Thank you.

## References

1. ^ Hong, Alice (2000). "Electric Field to Produce Spark in Air (Dielectric Breakdown)". The Physics Factbook.